1. Technical Field
The invention relates to time keeping devices. More particularly, the invention relates to enhanced compound pendulums that can be thermally and/or barometrically compensated, such as for a mechanical clock.
2. Description of the Prior Art
Historically, the gravity pendulum has been the most successful device for accurately regulating the timing of a mechanical clock. The frequency of such a simple pendulum is approximately proportional to the square root of the ratio of earth's gravity to length of the pendulum (f=2π√{square root over (l/g)}). Because the force of gravity is reasonably constant, keeping the period constant is largely a matter of keeping the length constant, which can be accomplished by careful selection of the materials and geometry, while paying special attention to expansion due to changes in temperature.
While an idealized pendulum has all of its mass concentrated at a point, real pendulum are actually a compound pendulums, with a distributed mass. In general, a compound pendulum has a longer period than a corresponding idealized pendulum, because of the extra moment of inertia contributed by the distribution of the mass.
Another potential accuracy problem of a gravity pendulum is that the period of the swing actually depends slightly on the amplitude. The frequency formula mentioned above is based on the assumption that the restoring force created by gravity is proportional to the angle of the bob from vertical, which is only an approximation. Actually, the restoring force is proportional to the sine of that angle. This difference is small as long as the angle is small, but to hold the frequency constant, the average amplitude of the swing must also be held constant.
Friction creates most of the difficulties in holding constant amplitude. While the greatest source of friction is often the pendulum motion through the air, there is also friction in the unlocking of the escapement, as well as friction in the suspension. Each of these sources of friction is variable. Also, the existence of any type of friction requires that energy be put back into the pendulum, to keep the pendulum going. This impulsion of the pendulum can be a major source of variability, because it is difficult to deliver the exact same impulse on each tick.
Another source of the error in a pendulum is the variation of the density of air, which changes the buoyancy of the bob. Because some of the weight of the bob is supported by floating in the surrounding air, the restoring force of gravity varies with the density. Because the density of the air depends on the barometric pressure, variations in pressure contribute to variability in, the rate of the pendulum.
Eliminating air around the pendulum can reduce several sources of variability because, while air is not only the source of the variable density problem, air is also the source of much of the friction. For this reason, most accurate clock pendulums at this time are operated in a partial vacuum.
It would be advantageous to provide a pendulum that has some of the same advantages, but without the complexities of maintaining a partial vacuum.
It would also be advantageous to provide a pendulum that has thermal compensation and/or barometric compensation, that is simple to construct, and that is more easily compensated than a conventional, single-bob pendulum.